A universal correction to higher spin entanglement entropy

TL;DR

This paper demonstrates that the second-order correction to entanglement entropy in 1+1D conformal field theories with W-algebra symmetry, deformed by a spin-three chemical potential, is universal and determined by operator product expansions and expectation values.

Contribution

It establishes a universal formula for the second-order correction to entanglement entropy in deformed W-algebra CFTs, explaining previous cross-model agreements.

Findings

The  correction is universal across different models.

The correction is determined by operator product expansions and expectation values.

The results match holographic computations involving higher spin black holes.

Abstract

We consider conformal field theories in 1+1 dimensions with W-algebra symmetries, deformed by a chemical potential \mu for the spin-three current. We show that the order \mu^2 correction to the Re'nyi and entanglement entropies of a single interval in the deformed theory, on the infinite spatial line and at finite temperature, is universal. The correction is completely determined by the operator product expansion of two spin-three currents, and by the expectation values of the stress tensor, its descendants and its composites, evaluated on the n-sheeted Riemann surface branched along the interval. This explains the recently found agreement of the order \mu^2 correction across distinct free field CFTs and higher spin black hole solutions holographically dual to CFTs with W-symmetry.